David Cameron has a “mandate and a duty” to continue as Prime Minister, Eurosceptic MPs and Cabinet members have said in an attempt to unite the party following the EU referendum.

More than 80 Eurosceptic Tory MPs – including every Cabinet minister who voted Leave – signed a letter addressed to Mr Cameron, urging him to remain as Prime Minister regardless of the referendum result.

"Please stay", say the Eurosceptics

However, scores of Conservative MPs are thought to have refused to sign the letter, which will intensify concerns in Downing Street that Mr Cameron’s most vocal opponents could still attempt to launch a vote of no confidence in the Prime Minister in the weeks after the vote.

The view in Labour HQ is that, if Britain does vote to leave, Jeremy Corbyn should call on David Cameron to resign, but senior figures believe that that may prove unnecessary because Cameron may announce his departure of his own accord.

In a speech several hours after most results were counted, Nigel Farage later said Mr Cameron should resign "immediately" if Brexit won what was still expected to be a knife-edge vote.

Eurosceptic Tories on Thursday began speaking about their “duty” to ensure “political stability” before the polls had even closed in what is only the third nationwide referendum in UK history.

A record 46.5million people were eligible to take part in Thursday’s vote and reports from across the country last night suggested a high national turnout.

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Senior figures from both the Tory Leave and Remain campaigns have in recent days started discussing how to bring the party back together and ensure that the Government continues to function in the days after the vote.

The letter, which was organised Tory MP Robert Syms and signed by Vote Leave leaders Boris Johnson and Michael Gove, was delivered to Mr Cameron as the polls closed at 10pm.

David and Samantha Cameron cast their votes in the EU Referendum

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Other Eurosceptic Cabinet ministers to have signed the letter include John Whittingdale, the Culture Secretary, Chris Grayling, the Leader of the Commons and Theresa Villiers, the Northern Ireland Secretary.

Priti Patel, the work and pensions minister who has been one of Mr Cameron’s most vocal critics during the referendum campaign, has also put her name to the letter.

Pro-Remain MPs and ministers have also signed the letter, sources said.

Matt's referendum cartoon

The letter states: “We who are supporters of Vote Leave and members of the Conservative Party thank you for giving the British people a choice of their destiny on 23 June.

“We believe that whatever the British people decide you have both a mandate and a duty to continue leading the nation implementing our 2015 manifesto.”

Mr Grayling said: “It's really important now that the Conservative Party unites and gets on with the job of governing the country.

David Cameron, campaigning for a Remain vote

"It has been a robust debate on a subject that both sides feel passionate about but we are facing a labour opposition that is more left wing and more extreme than any other in my lifetime. We must make sure that they don't get anywhere near power because of divisions in our ranks.

"There is a very strong view amongst conservative MPs that we need to move on and unite behind David Cameron."

Liam Fox, the former Defence Secretary, has also signed the letter and said the Conservative Party must find a way to “heal the divisions” caused by the referendum.

David Cameron and Boris Johnson face off on eve of referendum

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He said: “I have signed the letter. I think that after the referendum our first duty is to provide political stability, whatever the result, and find a way to heal the divisions within Britain and continue with a programme on which we are elected.”

The letter comes despite significant anger amongst Eurosceptic MPs about the way in which Mr Cameron and George Osborne, the Chancellor, conducted the referendum campaign.

Leave campaigners repeatedly accused the Prime Minister and Chancellor of “scaremongering” and attempting to win the vote by using “Project Fear” tactics.

Scores of Tory MPs were before the referendum considering writing letter to Graham Brady, the chairman of the 1922 Committee of backbenchers, calling for a vote of no confidence in the Prime Minister.

Although it is believed Mr Cameron would easily win any vote of no confidence, it would destabilise his leadership and lead to further disputes amongst Tory MPs, something his allies are desperate to avoid.

It is now believed Mr Cameron will delay a reshuffle until the Autumn. Sources say this is in part designed to “calm things down” over the summer months, with MPs waiting to see who will be offered jobs before publically questioning Mr Cameron’s leadership.

Another signatory to the letter added: “I’m not happy with the way David led his campaign, but the long-term future of the party is really important and this letter is very necessary at the moment. The party needs to come back together.”

Many Eurosceptics have voiced anger at Mr Osborne during the referendum campaign, particularly after his decision to publish a “Brexit budget” predicting tax rises and huge public spending cuts if Britain left the EU.

Meanwhile, it emerged that Downing Street is planning to announce whether it will give the go-ahead to the expansion of Heathrow Airport on the day after the publication of the Chilcot report into the Iraq War.

Sources have said that the decision on Heathrow will be announced on July 7, in a move that risks Number 10 being accused of "burying bad news" following the publication of the Iraq report.